As a corner of Elland Road erupted into one massed frenzy, 25,000-plus Yorkshiremen looked on shell-shocked.
The dream of an easy and comfortable home win to get their season up and running was turning into a nightmare. The Grecians had snatched the script from their big-name hosts, ripped it up and shoved it right down their throats.
As concern crept in and Leeds toiled, Exeter looked like they were going to pull off the impossible. But the smallest of mistakes will get punished at this level and, with Exeter tiring, Leeds created an overlap on the right and Crowe's cross was headed in by Beckford with Paul Jones caught in no man's land.
The relief of the home fans was tangible. The disappointment in the away end was understandable and was etched on the faces of Exeter's battle weary heroes. They had given their all and had done their fans proud, but it wasn't quite enough.
On the balance of play, few could argue the former Premier League outfit merited their win. They created a plethora of chances and could have won by a hatful, but, for work-rate, endeavour and sheer guts, only a cold-hearted Yorkshireman would not have had some sympathy for City come full-time.
As expected, the start was like the Alamo. Exeter repelled wave after wave of Leeds attacks and rode their luck at times as well. Beckford had already been denied by Jones - twice - and curled another shot narrowly wide before he broke the deadlock with the cutest of deft chips, following Ben Parker's electrifying burst from full-back.
The Grecians were struggling to get a hold in the game, despite having the extra man in midfield, and Leeds seemed to have spare men all over the park. Their passing and movement was slick, their pressing equally so and City found themselves pinned inside their own half for almost the entire first quarter.
Bertie Cozic did not make the most of one rare foray forward as he failed to spot Ryan Harley in acres of space on the right, but the Frenchman made amends moments later when he played in Corr.
The striker had time on his side, but rushed a half-volley that skewed horribly wide of the near post.
Beckford was denied by the woodwork as his brilliant dipping header came back off an upright from the outstanding Richard Snodgrass's cross, while Jones almost fumbled a Snodgrass cross into his own goal.
The longer the half went on, though, the more City came into the game. Harley struck a promising free-kick lazily into the wall, while the flame-haired midfielder's superb low cross was just beyond the reach of both Cozic and Corr.
The former Sheffield Wednesday and Swindon striker had another half-chance as Harley's corner fell to him at the back post, but the Irishman took too long to get his shot away and saw it blocked.
However, Exeter continued in the same vein after the break, but, with them enjoying their best spell of the game, Corr saw red and criminally lashed out at Doyle, who was holding his shirt. He could have no complaints.
Beckford twice chipped over the bar as Exeter acclimatised to a new 3-4-2 system, and introduced Craig McAllister and James Norwood from the bench, while Jason Crowe missed a great chance as Beckford's shot was well blocked by Richard Duffy and fell kindly for the full-back.
To their credit, the Grecians continued to play their football and when McAllister won his side a free-kick 25 yards from goal, City knew they had their chance.
Russell took it with both hands as he tapped the ball to Harley, who stopped it dead, and the former Bristol City playmaker curled a pearler into the far top corner.
Shane Higgs remained rooted to the spot and could only admire the quality of the strike from the impressive Russell, who had really grown into the game.
Leeds suddenly lost their way and were struggling to break down a City defence that held their shape admirably.
Until two minutes from time, when Snodgrass and Crowe ganged up on Scott Golbourne and Crowe chipped the ball into the six-yard box. Jones should have come and taken the lot. He didn't, and Beckford rose highest to head into a vacant goal.
As Exeter pressed for an equaliser, Norwood showed some brilliant skill on the right wing to win his side a free-kick.
Harley's deep cross was headed goalwards, but, as Norwood rushed in, he was perhaps put off by the imposing Higgs and the chance went begging.
It wasn't to be the dream debut the lively youngster would have dreamed of, nor was it the result Exeter desired. But, if this is the best that League One has to offer, then City have nothing to fear.
Phil Hay, the Yorkshire Evening Post's chief football writer's verdict on how the Leeds United players fared in the 2-1 win over Exeter City. www.yorkshireeveningpost.co.uk/
Jason Crowe: Pre-season proved that Crowe is an attacking asset, and his cross for the winning goal was delivered perfectly. Gave away the free-kick which led to Exeter's goal, however - 7/10
Patrick Kisnorbo: A lone striker like Barry Corr was never going to bulldoze Kisnorbo, and the Australian kept United's defence organised. There was little he could do to avert City's goal, which came from a set-piece - 7/10
Rui Marques: A solid show from Marques who looks happy in tandem with Kisnorbo. Even when Exeter gained a foothold, the centre of United's defence was reassuringly firm - 7/10
Ben Parker: The marauding run in the lead-up to Beckford's first strike was Parker at his best, covering ground directly and at pace. He lasted for only 28 minutes before a hamstring strain cut short his outing - 6/10
Robert Snodgrass: Industrious and worked tirelessly to keep Leeds in control of possession for the first 45 minutes. Also played his part in the attack which settled the match - 7/10
Jonathan Howson: He and Doyle ran the midfield before the break, a spell when Howson had the right idea with his passing if not always the execution. He was far less prominent in the second half - 6/10
Michael Doyle: Clearly likes the cut and thrust of the engine room and added a destructive edge to United's team. The range of his passing was impressive, though he faded slightly later on - 7/10
Bradley Johnson: A little careless in possession, and the jury is still out on whether Johnson is an effective option on the left wing. Caused a degree of danger but not as much as he would have liked - 6/10
Luciano Becchio: Deja vu for Becchio whose physical work up front helped make the best of Beckford's talents. He was responsible for the mundane graft which is so vital to Leeds - 6/10
Jermaine Beckford: Could United really do without this man? Took his goals brilliantly, hit the crossbar and could have scored twice more. Credit also for the way he chased the ball when isolated in the second half - 9/10
Substitutes: Andrew Hughes (for Parker, 28) - 6/10, Andy Robinson (for Johnson, 74) - 5/10, Enoch Showunmi (for Becchio, 84) - 6/10
Subs Unused: Ankergren, Grella, Prutton, Michalik.
Exeter City: Jones, Duffy, Seaborne, Taylor, Golbourne, Russell, Edwards (McAllister 61), Harley, Cozic (Sercombe 90), Stewart (Norwood 70), Corr. Subs Unused: Marriott, Tully, Burnell, Archibald-Henville.